We study the problem of minimizing the diameter of a graph by adding k shortcut edges, for speeding up communication in an existing network design. We develop constant-factor appro...
We show that for every connected graph G of diameter 3, the graph G3 has average degree 7 4 (G). We also provide an example showing that this bound is best possible. This resolv...
For z1, z2, z3 Zn, the tristance d3(z1, z2, z3) is a generalization of the L1-distance on Zn to a quantity that reflects the relative dispersion of three points rather than two. ...
The diameter of an undirected graph is the minimal number d such that there is a path between any two vertices of the graph of length at most d. The radius of a graph is the minim...
Edith Hemaspaandra, Lane A. Hemaspaandra, Till Tan...
We maintain the maximum spanning tree of a planar point set, as points are inserted or deleted, in O(log3 n) time per update in Mulmuley's expected-case model of dynamic geom...